Feature Encoding and Duplication in Gielis Curve Classification: A Superelliptic Frenet Perspective on Robustness

Feature encoding and duplication can affect classifier robustness even when representations contain equivalent information. We study these effects using 2500 synthetic three-dimensional Gielis curves obtained by radially scaling a fixed helix. A twelve-component superelliptic Frenet representation can be reconstructed from four radial statistics and one endpoint-sensitive angular moment. Nine representations are compared using support vector machines and random forests, five stratified holdouts, training-only cross-validation, and three paired radial-noise realizations per holdout. All configurations perfectly classify the original clean test data. At $\delta =0.10$, forests using the full descriptor, radial mean, and radial root-mean-square (RMS) attain $99.67\pm 0.11\%$, $99.97\pm 0.04\%$, and $99.81\pm 0.10\%$ accuracy, respectively. Repeating the radial RMS eight times also attains $99.81\pm 0.10\%$, showing sensitivity to redundant features. Dispersions are sample standard deviations across holdout means. A separate clean benchmark with shared exponent ranges and frequency-based labels separates the representations under fixed classifier settings. A sampled Euclidean square-root velocity function (SRVF) control is sensitive to noise but performs well on this harder clean task. The results do not establish a unique Frenet-specific robustness advantage and are limited to the tested synthetic datasets and perturbations.